Subgroups — C₂×C₆₇×#3147 #30739883

Order 17152.

3366 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₇	C₂	1	4	yes	maximal, complemented
2	C₂×#532×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3147	C₂	1	16	yes	maximal, direct product factor
4	C₂×#495×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#494×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#493×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#492×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₇	C₂²	1	4	yes	—
10	C₂×#135×C₆₇	—	2	32	no	—
11	C₂×#135×C₆₇	C₂²	1	32	yes	complemented
12	C₂²×Q₁₆×C₆₇	C₂²	1	4	yes	—
13	C₂²×SD₁₆×C₆₇	C₂²	1	8	yes	—
14	C₂²×D₈×C₆₇	C₂²	1	4	yes	—
15	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
16	#532×C₆₇	—	2	8	no	—
17	#532×C₆₇	C₂²	1	16	yes	complemented
18	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
19	C₂×#127×C₆₇	C₂²	1	2	yes	—
20	C₂×#124×C₆₇	C₂²	1	4	yes	—
21	C₂×#121×C₆₇	—	2	4	no	—
22	C₂×C₄×D₄×C₆₇	—	2	4	no	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	#495×C₆₇	C₂²	1	32	yes	complemented
25	#494×C₆₇	C₂²	1	8	yes	complemented
26	#493×C₆₇	C₂²	1	8	yes	complemented
27	#492×C₆₇	C₂²	1	16	yes	complemented
28	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₆₇	C₂²	1	8	yes	complemented
32	C₂×#41×C₆₇	—	2	8	no	—
33	C₂×#41×C₆₇	—	2	32	no	—
34	C₂×#41×C₆₇	C₂³	1	16	yes	—
35	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
36	C₂²×D₄×C₆₇	—	2	4	no	—
37	C₂²×D₄×C₆₇	—	2	4	no	—
38	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₆₇	—	2	4	no	—
40	C₂³×C₄×C₆₇	D₄	1	2	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
42	#135×C₆₇	—	2	128	no	—
43	C₂×Q₁₆×C₆₇	—	2	16	no	—
44	C₂×Q₁₆×C₆₇	C₂³	1	16	yes	—
45	C₂×SD₁₆×C₆₇	—	2	32	no	—
46	C₂×SD₁₆×C₆₇	C₂³	1	32	yes	—
47	C₂×D₈×C₆₇	—	2	16	no	—
48	C₂×D₈×C₆₇	C₂³	1	16	yes	—
49	C₂²×C₈×C₆₇	D₄	1	16	yes	complemented
50	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
53	C₄⋊Q₈×C₆₇	—	2	4	no	—
54	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
55	#127×C₆₇	—	2	4	no	—
56	#127×C₆₇	C₂³	1	8	yes	—
57	#124×C₆₇	—	2	8	no	—
58	#124×C₆₇	C₂³	1	16	yes	—
59	#121×C₆₇	—	2	32	no	—
60	C₄×D₄×C₆₇	—	2	32	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
63	C₂×C₄²×C₆₇	D₄	1	4	yes	—
64	C₂×C₄²×C₆₇	D₄	1	2	yes	—
65	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
68	C₄×C₈×C₆₇	C₂³	1	4	yes	—
69	C₄×C₈×C₆₇	C₂³	1	4	yes	—
70	C₄×C₈×C₆₇	C₂³	1	8	yes	—
71	C₂⁴×C₆₇	—	2	4	no	—
72	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
73	#41×C₆₇	—	2	64	no	—
74	#41×C₆₇	—	4	32	no	—
75	C₂×Q₈×C₆₇	—	2	4	no	—
76	C₂×Q₈×C₆₇	—	2	16	no	—
77	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
78	C₂×D₄×C₆₇	—	2	16	no	—
79	C₂×D₄×C₆₇	—	2	16	no	—
80	C₂×D₄×C₆₇	—	2	16	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	4	16	no	—
83	C₂×D₄×C₆₇	—	4	16	no	—
84	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
85	C₂²×C₄×C₆₇	—	2	8	no	—
86	C₂²×C₄×C₆₇	—	2	4	no	—
87	C₂²×C₄×C₆₇	—	2	16	no	—
88	C₂²×C₄×C₆₇	—	4	16	no	—
89	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
97	Q₁₆×C₆₇	—	2	32	no	—
98	SD₁₆×C₆₇	—	2	64	no	—
99	D₈×C₆₇	—	2	32	no	—
100	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
101	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
102	C₂×C₈×C₆₇	C₂×D₄	1	32	yes	complemented
103	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
104	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
105	C₄⋊C₄×C₆₇	—	2	16	no	—
106	C₂²⋊C₄×C₆₇	—	2	32	no	—
107	C₄²×C₆₇	C₂×D₄	1	8	yes	—
108	C₄²×C₆₇	C₂×D₄	1	2	yes	—
109	C₄²×C₆₇	C₂×D₄	1	2	yes	—
110	C₄²×C₆₇	C₂⁴	1	2	yes	—
111	C₄²×C₆₇	C₂⁴	1	2	yes	—
112	C₂³×C₆₇	—	2	4	no	—
113	C₂³×C₆₇	—	2	8	no	—
114	C₂³×C₆₇	—	4	8	no	—
115	C₂³×C₆₇	—	4	16	no	—
116	C₂³×C₆₇	#127	1	4	yes	—
117	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
118	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
119	Q₈×C₆₇	—	2	16	no	—
120	Q₈×C₆₇	—	4	8	no	—
121	D₄×C₆₇	—	2	16	no	—
122	D₄×C₆₇	—	4	32	no	—
123	D₄×C₆₇	—	4	8	no	—
124	D₄×C₆₇	—	4	32	no	—
125	C₂×C₄×C₆₇	—	2	4	no	—
126	C₂×C₄×C₆₇	—	2	16	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	—	4	8	no	—
129	C₂×C₄×C₆₇	—	4	32	no	—
130	C₂×C₄×C₆₇	#127	1	4	yes	—
131	C₂×C₄×C₆₇	#127	1	8	yes	—
132	C₂×C₄×C₆₇	#135	1	8	yes	complemented
133	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
134	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
135	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
137	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
138	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
139	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
140	C₈×C₆₇	C₂²×D₄	1	8	yes	—
141	C₈×C₆₇	C₂²×D₄	1	8	yes	—
142	C₂²×C₆₇	—	2	8	no	—
143	C₂²×C₆₇	—	2	4	no	—
144	C₂²×C₆₇	—	4	8	no	—
145	C₂²×C₆₇	—	4	16	no	—
146	C₂²×C₆₇	—	8	16	no	—
147	C₂²×C₆₇	C₂×#127	1	4	yes	—
148	C₂²×C₆₇	C₂×#127	1	2	yes	—
149	C₂²×C₆₇	C₂×#135	1	4	yes	—
150	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
151	C₄×C₆₇	—	2	4	no	—
152	C₄×C₆₇	—	4	8	no	—
153	C₄×C₆₇	C₂×#127	1	4	yes	—
154	C₄×C₆₇	C₂×#127	1	2	yes	—
155	C₄×C₆₇	C₂×#135	1	8	yes	complemented
156	C₄×C₆₇	C₂³×D₄	1	2	yes	—
157	C₂×#3147	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂×C₆₇	—	2	4	no	—
159	C₂×C₆₇	—	8	8	no	—
160	C₂×C₆₇	#3147	1	4	yes	direct product factor
161	C₂×C₆₇	C₂²×#127	1	1	yes	characteristic
162	C₂×C₆₇	C₂²×#135	1	2	yes	—
163	C₂²×#135	C₂×C₆₇	1	4	yes	complemented
164	C₂×#532	C₂×C₆₇	1	2	yes	complemented
165	#3147	C₂×C₆₇	1	16	yes	direct product factor
166	C₂×#495	C₂×C₆₇	1	4	yes	complemented
167	C₂×#494	C₂×C₆₇	1	1	yes	characteristic, complemented
168	C₂×#493	C₂×C₆₇	1	1	yes	characteristic, complemented
169	C₂×#492	C₂×C₆₇	1	2	yes	complemented
170	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
171	C₆₇	C₂×#3147	1	1	yes	characteristic, direct product factor, Sylow
172	C₂²×#41	C₂²×C₆₇	1	4	yes	—
173	C₂×#135	—	2	32	no	—
174	C₂×#135	C₂²×C₆₇	1	32	yes	complemented
175	C₂²×Q₁₆	C₂²×C₆₇	1	4	yes	—
176	C₂²×SD₁₆	C₂²×C₆₇	1	8	yes	—
177	C₂²×D₈	C₂²×C₆₇	1	4	yes	—
178	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
179	#532	—	2	8	no	—
180	#532	C₂²×C₆₇	1	16	yes	complemented
181	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
182	C₂×#127	C₂²×C₆₇	1	2	yes	—
183	C₂×#124	C₂²×C₆₇	1	4	yes	—
184	C₂×#121	—	2	4	no	—
185	C₂×C₄×D₄	—	2	4	no	—
186	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
187	#495	C₂²×C₆₇	1	32	yes	complemented
188	#494	C₂²×C₆₇	1	8	yes	complemented
189	#493	C₂²×C₆₇	1	8	yes	complemented
190	#492	C₂²×C₆₇	1	16	yes	complemented
191	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₆₇	1	8	yes	complemented
195	C₂×#41	—	2	8	no	—
196	C₂×#41	—	2	32	no	—
197	C₂×#41	C₂³×C₆₇	1	16	yes	—
198	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	—	2	4	no	—
201	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
202	C₂³×C₄	—	2	4	no	—
203	C₂³×C₄	D₄×C₆₇	1	2	yes	—
204	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
205	#135	—	2	128	no	—
206	C₂×Q₁₆	—	2	16	no	—
207	C₂×Q₁₆	C₂³×C₆₇	1	16	yes	—
208	C₂×SD₁₆	—	2	32	no	—
209	C₂×SD₁₆	C₂³×C₆₇	1	32	yes	—
210	C₂×D₈	—	2	16	no	—
211	C₂×D₈	C₂³×C₆₇	1	16	yes	—
212	C₂²×C₈	D₄×C₆₇	1	16	yes	complemented
213	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
214	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
215	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
216	C₄⋊Q₈	—	2	4	no	—
217	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
218	#127	—	2	4	no	—
219	#127	C₂³×C₆₇	1	8	yes	—
220	#124	—	2	8	no	—
221	#124	C₂³×C₆₇	1	16	yes	—
222	#121	—	2	32	no	—
223	C₄×D₄	—	2	32	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₂²⋊C₄	—	2	8	no	—
226	C₂×C₄²	D₄×C₆₇	1	2	yes	—
227	C₂×C₄²	D₄×C₆₇	1	4	yes	—
228	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
231	C₄×C₈	C₂³×C₆₇	1	4	yes	—
232	C₄×C₈	C₂³×C₆₇	1	4	yes	—
233	C₄×C₈	C₂³×C₆₇	1	8	yes	—
234	C₂⁴	—	2	4	no	—
235	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
236	#41	—	2	64	no	—
237	#41	—	4	32	no	—
238	C₂×Q₈	—	2	4	no	—
239	C₂×Q₈	—	2	16	no	—
240	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
241	C₂×D₄	—	2	16	no	—
242	C₂×D₄	—	2	16	no	—
243	C₂×D₄	—	2	16	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	4	16	no	—
246	C₂×D₄	—	4	16	no	—
247	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	4	16	no	—
252	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
254	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
257	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
258	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
259	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
260	Q₁₆	—	2	32	no	—
261	SD₁₆	—	2	64	no	—
262	D₈	—	2	32	no	—
263	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
264	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
265	C₂×C₈	C₂×D₄×C₆₇	1	32	yes	complemented
266	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
267	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
268	C₄⋊C₄	—	2	16	no	—
269	C₂²⋊C₄	—	2	32	no	—
270	C₄²	C₂×D₄×C₆₇	1	8	yes	—
271	C₄²	C₂×D₄×C₆₇	1	2	yes	—
272	C₄²	C₂×D₄×C₆₇	1	2	yes	—
273	C₄²	C₂⁴×C₆₇	1	2	yes	—
274	C₄²	C₂⁴×C₆₇	1	2	yes	—
275	C₂³	—	2	4	no	—
276	C₂³	—	2	8	no	—
277	C₂³	—	4	8	no	—
278	C₂³	—	4	16	no	—
279	C₂³	#127×C₆₇	1	4	yes	—
280	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
281	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
282	Q₈	—	2	16	no	—
283	Q₈	—	4	8	no	—
284	D₄	—	2	16	no	—
285	D₄	—	4	32	no	—
286	D₄	—	4	8	no	—
287	D₄	—	4	32	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	16	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	4	8	no	—
292	C₂×C₄	—	4	32	no	—
293	C₂×C₄	#127×C₆₇	1	4	yes	—
294	C₂×C₄	#127×C₆₇	1	8	yes	—
295	C₂×C₄	#135×C₆₇	1	8	yes	complemented
296	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
297	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
298	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
299	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
300	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
301	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
302	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
303	C₈	C₂²×D₄×C₆₇	1	8	yes	—
304	C₈	C₂²×D₄×C₆₇	1	8	yes	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	8	no	—
307	C₂²	—	4	16	no	—
308	C₂²	—	4	8	no	—
309	C₂²	—	8	16	no	—
310	C₂²	C₂×#127×C₆₇	1	4	yes	—
311	C₂²	C₂×#127×C₆₇	1	2	yes	—
312	C₂²	C₂×#135×C₆₇	1	4	yes	—
313	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
314	C₄	—	2	4	no	—
315	C₄	—	4	8	no	—
316	C₄	C₂×#127×C₆₇	1	4	yes	—
317	C₄	C₂×#127×C₆₇	1	2	yes	—
318	C₄	C₂×#135×C₆₇	1	8	yes	complemented
319	C₄	C₂³×D₄×C₆₇	1	2	yes	—
320	C₂	—	2	4	no	—
321	C₂	—	8	8	no	—
322	C₂	C₆₇×#3147	1	4	yes	direct product factor
323	C₂	C₂²×#127×C₆₇	1	1	yes	characteristic
324	C₂	C₂²×#135×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×#135×C₆₇	C₂	semidirect
2. C₂×#532×C₆₇	C₂	semidirect
3. C₆₇×#3147	C₂	direct (N × H)
4. C₂×#495×C₆₇	C₂	semidirect
5. C₂×#494×C₆₇	C₂	semidirect
6. C₂×#493×C₆₇	C₂	semidirect
7. C₂×#492×C₆₇	C₂	semidirect
8. C₂²×C₄×C₈×C₆₇	C₂	semidirect
11. C₂×#135×C₆₇	C₂²	semidirect
17. #532×C₆₇	C₂²	semidirect
24. #495×C₆₇	C₂²	semidirect
25. #494×C₆₇	C₂²	semidirect
26. #493×C₆₇	C₂²	semidirect
27. #492×C₆₇	C₂²	semidirect
31. C₂×C₄×C₈×C₆₇	C₂²	semidirect
49. C₂²×C₈×C₆₇	D₄	semidirect
102. C₂×C₈×C₆₇	C₂×D₄	semidirect
132. C₂×C₄×C₆₇	#135	semidirect
155. C₄×C₆₇	C₂×#135	semidirect
157. C₂×#3147	C₆₇	direct (N × H)
160. C₂×C₆₇	#3147	direct (N × H)
163. C₂²×#135	C₂×C₆₇	semidirect
164. C₂×#532	C₂×C₆₇	semidirect
165. #3147	C₂×C₆₇	direct (N × H)
166. C₂×#495	C₂×C₆₇	semidirect
167. C₂×#494	C₂×C₆₇	semidirect
168. C₂×#493	C₂×C₆₇	semidirect
169. C₂×#492	C₂×C₆₇	semidirect
170. C₂²×C₄×C₈	C₂×C₆₇	semidirect
171. C₆₇	C₂×#3147	direct (N × H)
174. C₂×#135	C₂²×C₆₇	semidirect
180. #532	C₂²×C₆₇	semidirect
187. #495	C₂²×C₆₇	semidirect
188. #494	C₂²×C₆₇	semidirect
189. #493	C₂²×C₆₇	semidirect
190. #492	C₂²×C₆₇	semidirect
194. C₂×C₄×C₈	C₂²×C₆₇	semidirect
212. C₂²×C₈	D₄×C₆₇	semidirect
265. C₂×C₈	C₂×D₄×C₆₇	semidirect
295. C₂×C₄	#135×C₆₇	semidirect
318. C₄	C₂×#135×C₆₇	semidirect
322. C₂	C₆₇×#3147	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#135×C₆₇	2
C₂×#532×C₆₇	2
C₆₇×#3147	2
C₂×#495×C₆₇	2
C₂×#494×C₆₇	2
C₂×#493×C₆₇	2
C₂×#492×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂×#3147	67

Subgroups — C2×C67×#3147 #30739883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3147 #30739883